Mixed Work with Leaving Worker – UGC NET Question

The daily work rates of A, B and C are 1/10, 1/15 and 1/30 respectively. Working together, their combined rate is 1/10 + 1/15 + 1/30, which simplifies to 1/5 of the work per day. In the first 2 days, they therefore complete 2 × 1/5 = 2/5 of the work. The remaining 3/5 of the work is then done by B and C alone, whose combined rate is 1/15 + 1/30 = 1/10. At this rate, they need (3/5) ÷ (1/10) = 6 more days. Adding the initial 2 days gives a total of 8 days to finish the work.

Option A:
Option A correctly adds the contributions in the two phases: an initial phase with three workers and a second phase with two workers. It respects the different group rates and sums the corresponding time intervals to reach 8 days.

Option B:
Option B, 7 days, underestimates the time and would require the second phase to progress faster than the combined rate of B and C allows.

Option C:
Option C, 6 days, is only the time needed for B and C to complete 3/5 of the work, not including the first 2 days already spent by all three.

Option D:
Option D, 9 days, overestimates the total time and suggests a slower rate than actually achieved by the workers as a group.